Comparative Analysis of Nonlinear Models from Different Domains: A Case Study on the Quality of Groundwater in an Alluvial Aquifer in Northwestern Croatia

In groundwater quality analysis, nonlinear models are typically used, with domains spanning the entire real number line. In this study, alongside these models (Logistic, Gompertz and Richards), nonlinear models defined based on functions whose domain is only the positive part of the real number line are presented (Michaelis–Menten, Hill 1 and 2 and Rosin–Rammler 1 and 2). Two case studies were observed in the paper: (i) the dependence of nitrate concentration on the pumping rate in the Bartolovec wellfield, and (ii) the dependence of nitrate concentration on the distance from the source of pollution in the Varaždin wellfield. Both wellfields are located in the alluvial aquifer in northwestern Croatia. In this way, the curves obtained on the basis of the mentioned mathematical functions were fitted to the experimental data. The results show a good fit, so that the values of the coefficients of determination R2 are greater than 0.82 for the case study (i) and greater than 0.96 for the case study (ii). Since the models differ in the number of parameters (e.g., three parameters for Michaelis–Menten and five parameters for Rosin–Rammler), the corrected Akaike information criterion (AICc) was used for their comparison. In this way, the best fit for the case study (i) was obtained for the Rosin–Rammler 1 model, while for the case study (ii), it was for the Hill 1 model. A t-test was performed for all models, and they can be considered reliable at a significance level of 0.05. However, t-values and p-values were also calculated for each parameter of each model. Based on these results, it is concluded that all model parameters can be considered reliable at a significance level of 0.05 only for the Hill 1 and Rosin–Rammler 1 models in both case studies. For this reason, these models can generally be considered the best fit to the experimental data. The study demonstrates the superiority of nonlinear models with domains restricted to positive real numbers (e.g., Hill 1, Rosin–Rammler 1) over traditional models (e.g., Logistic, Richards) in groundwater quality analysis. These findings offer practical tools for predicting contaminant extremes (e.g., maximum/minimum concentrations) and optimizing groundwater management strategies.